Wang Yong owes the bank $\$8500$. To repay the debt, he paid a fixed amount back to the bank each month. After $12$ months, his remaining debt was $\$6460$. How much did Wang Yong pay each month? $\$$
Answer: Let's say that Wang Yong pays $V$ dollars back to the bank each month. Then, he pays $V\cdot T$ dollars in $T$ months. In addition, we know that his original debt was $\$8500$. Wang Yong's remaining debt is found by taking the original debt and subtracting from it the money he already paid back. We can express this with the equation $R=8500-V\cdot T$, where: $R$ represents Wang Yong's remaining debt at a given time (in dollars) $V$ represents Wang Yong's monthly payment to the bank (in dollars) $T$ represents the time (in months) We know that after $12$ months $(T={12})$, Wang Yong's remaining debt was $\$6460$ $(R={6460})$. Let's plug these values into the equation to find the value of $V$. $ \begin{aligned}{6460}&=8500-V\cdot{12}\\ 12V&=2040\\ V&=170\end{aligned}$ Therefore, Wang Yong paid the bank $\$170$ each month. To find how long it took Wang Yong to pay back his entire debt, we can plug $R=0$ into the equation and solve for $T$. $ \begin{aligned}0&=8500-170T\\ 170T&=8500\\ T&=50\end{aligned}$ Wang Yong paid the bank $\$170$ each month. It took Wang Yong $50$ months to pay back his entire debt.